It seems like if Tsunade had Minato a few years before Dan died the timeline would work out.
Minato died at the nine tails attack which took place 13 years before part 1 since naruto was born shortly before the fox was sealed and he is 13 in part 1. It would seem he became hokage shortly after Kakashi Gaiden and the fox attack happened that same year.
If at present Tsunade is 54 and naruto is 16 the fox attacked when Tsunade was 38. Dan died when he and Tsunade were 27 or 11 years before Minatos death.
If Tsunade and Dan had Minato when they were 19, an age that is not far fetched in our society and especially considering their war torn one, Minato would have been 8 at the time of Dans death and 19 at the time of his own death.
Naruto was born in October, late enough in the year where Kakashi gaiden could have happened, Minato would have been without a group of students, and the war would have tipped in konohas favor, leading to a good time for a transition of power.
I like this idea would be interesting to see Narutos reaction to it if it was true